Theorems

postulate1-3--given AB and a # r between 0 and 180, there is exactly one ray w/ endpoint

A,extending on each side ofAB, such that the

measure of the angle formed is r

postulate1-4--if r is in the interior of pqs,then Mpqr Mrqs=Mpqs.if Mpqr Mrqs then R is in thr interior of angle pqs

postulate 2-2--through any 3 points not on the same line there is exactly one plane

law of detachment--if P--*Q is a true conditional and P is true,then Q is true

law of syllogism--if P--*Q and Q--*R are true conditionals,then P--*R is also true

theorem2-1--congruence of segments is reflexive,symmetric and transitive

theorem2-2--if 2 angles form a linear pair, then they r supplementary angles

theorem2-3--congruence of angles is reflexive,symmetric,and transitive

theorem2-4--angles supplementary to the same angle or to the congruent angles r congruent

theorem2-5--angles complementary to the same angle or to congruent angles r congruent

theorem2-6--all right angles r congruent

theorem2-7--vertical angles r congruent

theorem2-8--perpindicular lines intersect to form 4 right angles

skew lines-2 lines r skew if they don’t intersect and r not in the samn plane

postulate3-1-- if 2 // lines r cut by a transversal,then each pair of corresponding angles is congruent

theorem3-1--if 2 // lines r cut by a transversal,then each pair of alternate interior angles in congruent

postulate1-3--given AB and a # r between 0 and 180, there is exactly one ray w/ endpoint

A,extending on each side ofAB, such that the

measure of the angle formed is r

postulate1-4--if r is in the interior of pqs,then Mpqr Mrqs=Mpqs.if Mpqr Mrqs then R is in thr interior of angle pqs

postulate 2-2--through any 3 points not on the same line there is exactly one plane

law of detachment--if P--*Q is a true conditional and P is true,then Q is true

law of syllogism--if P--*Q and Q--*R are true conditionals,then P--*R is also true

theorem2-1--congruence of segments is reflexive,symmetric and transitive

theorem2-2--if 2 angles form a linear pair, then they r supplementary angles

theorem2-3--congruence of angles is reflexive,symmetric,and transitive

theorem2-4--angles supplementary to the same angle or to the congruent angles r congruent

theorem2-5--angles complementary to the same angle or to congruent angles r congruent

theorem2-6--all right angles r congruent

theorem2-7--vertical angles r congruent

theorem2-8--perpindicular lines intersect to form 4 right angles

skew lines-2 lines r skew if they don’t intersect and r not in the samn plane

postulate3-1-- if 2 // lines r cut by a transversal,then each pair of corresponding angles is congruent

theorem3-1--if 2 // lines r cut by a transversal,then each pair of alternate interior angles in congruent

theorem3-2--if 2 // lines r cut by a transversal,then each pair of consec. int. angles is supp.

theorem3-3--if 2 // lines r cut by a transversal,then each pair of alternate ext. angles is congruent

theorem3-4--in a plane,if a line is perp. to 1 of 2 // lines,then it is perp. to the other

postulate3-4--2 nonvertical lines have the same slope if and only if they r //.

postulate3-5--2 nonvertical lines r perp. if and only if the product of their slopes is -1

theorem4-3--the measure of an exterior angle of a triangle is equal to the sum of the

measures of the 2 remote interior angles

CPCTC- 2 triangles r congruent if and only if their corresponding parts r congruent

theorem4-4--congruence of triangles is reflexive,transitive and symmetric

theorem4-6--if 2 sides of a triangle r congruent,then the angles opp. the sides r congruent

theorem4-7--if 2 angles of a triangle r congruent,then the sides opp. those angles r congruent

theorem4-3--a triangle is equilateral if and only if it is equiangular

theorem5-1 a point on the perp. bisector of a seg. is equidistant from the endpoints of the seg.

theorem5-2--a point equidistant from the endpoints of a seg. lies in the perp. bisector of the seg.

theorem5-3--a point on the bisector of an angle is equidistant from the sides of the angle

theorem5-4--a point in the interior of or on an angle and equidistant from the sides of an

angle lies on the bisector of the angle

theorem5-5--if the legs of 1 rt. triangle r congruent to the corr. legs of another rt.

triangle, then the triangles r congruent

theorem3-3--if 2 // lines r cut by a transversal,then each pair of alternate ext. angles is congruent

theorem3-4--in a plane,if a line is perp. to 1 of 2 // lines,then it is perp. to the other

postulate3-4--2 nonvertical lines have the same slope if and only if they r //.

postulate3-5--2 nonvertical lines r perp. if and only if the product of their slopes is -1

theorem4-3--the measure of an exterior angle of a triangle is equal to the sum of the

measures of the 2 remote interior angles

CPCTC- 2 triangles r congruent if and only if their corresponding parts r congruent

theorem4-4--congruence of triangles is reflexive,transitive and symmetric

theorem4-6--if 2 sides of a triangle r congruent,then the angles opp. the sides r congruent

theorem4-7--if 2 angles of a triangle r congruent,then the sides opp. those angles r congruent

theorem4-3--a triangle is equilateral if and only if it is equiangular

theorem5-1 a point on the perp. bisector of a seg. is equidistant from the endpoints of the seg.

theorem5-2--a point equidistant from the endpoints of a seg. lies in the perp. bisector of the seg.

theorem5-3--a point on the bisector of an angle is equidistant from the sides of the angle

theorem5-4--a point in the interior of or on an angle and equidistant from the sides of an

angle lies on the bisector of the angle

theorem5-5--if the legs of 1 rt. triangle r congruent to the corr. legs of another rt.

triangle, then the triangles r congruent